Do we assume they come to the river on the same side? If not, then we one brother crosses to other other side, then the other brother gets into the boat and crosses too.
Do they need to remain on the other side of the river? If not, then one brother crosses and returns, then the other brother crosses. Both brother will have gone to the other side.

Brother 1 crosses the river, moves the boat upstream, brother 2 is awaiting to catch the boat at a narrower section of the river as brother 1 lets the boat float back down the river. Brother 2 crosses the river.

There's no mention of them being on the same side of the river. So the brother on the side of the river with the boat goes across, then the other brother gets in the boat and goes to the other side. Both brothers have crossed the river to the other side from where they started.